Limit periodic Schur algorithms,the case 441-1441-1441-1

We show that if a function bounded in the unit disk gives rise to a limit periodic Schur algorithm with ||=1, d_n,< then the function can be continued analytically to a meromorphic function in the entire plane except, possibly, for an essential singularity at z=–1. The lpS provides a very good approximation to the function.This research was supported in part by the US National Science Foundation under Grant DMS-9103141.